The Estimation of Gamma
THE ESTIMATION OF GAMMA
Martin Lally
School of Economics and Finance
Victoria University of Wellington
23 November 2013
CONTENTS
Executive Summary3
1. Introduction6
2. Background6
2.1 The Mechanics of Dividend Imputation6
2.2 The Role of Imputation Credits in the Officer CAPM9
3. Estimating the Utilisation Rate12
3.1 The Definition of U12
3.2 The Role of Foreign Investors14
3.3 The Equity Ownership Approach16
3.4 The Imputation Credit Redemption Rate16
3.5 The Use of Market Prices20
3.6An Alternative Interpretation of the Market Evidence30
3.7 The Views of Practitioners32
3.8 Other Approaches37
3.9A Test for Reasonableness38
3.10Summary47
4. Estimating the Distribution Rate49
4.1 The AER’s Approach49
4.2 Alternative Empirical Approaches50
4.3 Theoretical Approaches53
4.4 Summary54
5. Conclusions54
Appendix 1: Terms of Reference57
Appendix 2: The Officer CAPM62
References64
EXECUTIVE SUMMARY
In August 2013 the AER released draft guidelines for the setting of WACC in future determinations. These guidelines include a method for estimating the value of gamma, of 0.50, constituting the product of a distribution rate of 0.7 and a utilisation rate (U)of 0.70. This paper seeks to critically review the AER’s conclusions and to address a number of related questions posed by the AER relating to the definition of gamma, the role of foreign investors, and the use of data around dividend ex-days to estimate the utilisation rate. The conclusions are as follows.
In respect of U, there are five possible approaches to estimating it. The first of these arises from the definition of the parameter as a weighted average across all investors; coupled with ignoring foreigners (consistent with the Officer CAPM), this yields an estimate of 1 (the utilisation rate of local investors). The second possibility also arises from the definition of the parameter, but with recognition of foreigners, and leads to an estimate of about 0.70 (the proportion of Australian equities held by Australians). The thirdpossibility is to use the proportion of credits that are redeemed with the Australian tax authority by all investors, and leads to an estimate of about 0.40 to 0.80, with a midpoint of 0.60. The fourth possibility is to use market prices, from cum and ex-dividend share prices, simultaneous share and futures prices, simultaneous share index and futures prices, and regressions of returns on imputation credit yields. Using results from post July 2000, and using the parameter estimates favoured by the authors where there is variation, the results are 0.40, 0.13, 0.64, and -2.00. If the last result is ignored, on the grounds of complete implausibility, the average is 0.39. The fifth possibility is to draw upon surveys of market practitioners, which reveals a trend towards explicit recognition of the credits, with the latest evidence suggesting a value for U of 0.75 amongst those who make explicit adjustments and the rest generally appear to believe that U is positive despite not making explicit adjustments. So, it does not produce a point estimate.
In my view, the most important requirements in selecting a methodology for estimating U are that the estimate be consistent with the definition of U, as a value-weighted average over the utilisation rates of all investors who are relevant to the Officer CAPM, that the parameter estimate is likely to give rise to an estimated cost of equity from the Officer model that lies within the bounds arising from either complete segmentation or complete integration of equity markets, and that the estimate is reasonably precise. The first approach described in the previous paragraph satisfies each of these requirements and is therefore recommended. The second approach described in the previous paragraph satisfies the third of these requirements, but not the first because it recognises foreign investors and not the second in the sense that its associated estimate of U would give rise to implausibly high costs of equity; it is therefore ranked second. The third approach (the proportion of credits redeemed with the tax authorities) is similar to the second but lacks its precision and therefore does not satisfy any of these requirements. The fourth approach (using market prices) does not satisfy any of these requirements, because it is not a value-weighted average over all investors, its estimate of U would give rise to implausibly high costs of equity, and the estimate is very imprecise in the sense that the approach generates a wide range of estimates depending upon the specific methodology and data used, the estimates from the dividend drop-off studies may also reflect broader anomalies unrelated to tax issues, it is exposed to the actions of a small and unrepresentative set of investors, and it is exposed to microstructure effects such as the bid-ask bounce. It also produces ancillary results relating to the valuation of cash dividends that are inconsistent with the Officer model. The fifth approach does not produce a point estimate. Using the three criteria described above, my preferred estimate is 1 from the first approach and my second preference is 0.70 from the second approach. If these three criteria were rejected, I would favour use of the results from the first four approaches, with values of 1, 0.70, 0.60, and 0.39; the problems associated with the third and fourth methods warrant a lower weighting than on the other methods and therefore an estimate for U of about 0.80.
In respect of the distribution rate, the various theory-based arguments (all for a distribution rate of 1) are not justified, and therefore an empirical estimate is warranted. Within the Officer model, the distribution rate is firm specific. However, the use of firm-specific estimates is ruled out by the resulting incentives of firms to manipulate their dividend levels. The choice then lies between an industry average and a market average. Industry averages are likely to be an ongoing source of contention, involving which firms to choose and how much historical data to use. These difficulties are absent from a market average but there is considerable variation in the rate across firms and therefore the market-wide average could be a poor indicator of the situation for any industry. So, the appropriate choice is not clear but I favour the market-wide average. Finally, since the relevant distribution rate is the expected future rate and historical data reveals that a significant proportion of credits have not been distributed, it might be argued that they eventually will be and therefore the expected future distribution rate must exceed the historical rate. However, there is no strong theoretical argument for eventual distribution and therefore historical experience must be favoured as an estimator for the future. Invoking the historical market-wide data, from both the ATO and from annual reports, this points to an estimate for the distribution rate of at least 70%.
Having offered estimates for U and the distribution rate, the estimate of gamma is the product of these. My preferred estimate for U is 1 from the first approach described above and, coupled with my estimate for the distribution rate of at least 0.70, yields an estimate for gamma of at least 0.70. My second preference in estimating U is 0.70 from the second approach described above and, coupled with my estimate for the distribution rate of at least 0.70, yields an estimate for gamma of at least 0.50. My third preference in estimating U is about 0.80, as described above, and, coupled with my estimate for the distribution rate of at least 0.70, yields an estimate for gamma of at least 0.56.
- Introduction
In August 2013 the AER (2013) released draft guidelines for the setting of WACC in future determinations. These guidelines include a method for estimating the value of gamma, of 0.50, constituting the product of a distribution rate of 0.7 and a utilisation rate(U)of 0.70. This paper seeks to critically review the AER’s conclusions and to address a number of related questions posed by the AER relating to the definition of gamma, the role of foreign investors, and the use of data around dividend ex-days to estimate the utilisation rate(see the Terms of Reference in Appendix 1).
- Background
2.1 The Mechanics of Dividend Imputation
Consider a firm that generated taxable income of $10m, paid company tax of $3m (at the corporate tax rate of 30%), leaving $7m, and then paid a dividend of $4m. Prior to dividend imputation being adopted in Australia, the recipients of the dividends would have paid personal tax on the dividends in accordance with their marginal tax rate. So, if this was 35% for all such shareholders, the personal tax paid would have been 35% of $4m ($1.4m). Thus, two layers of tax are paid: company tax followed by personal tax when dividends are paid.
Dividend Imputation is designed to reduce the tax to only one layer, by treating company taxes that lie behind a dividend as a pre-payment of personal tax by companies on behalf of their shareholders. Crucial to this is to decide how much of the company taxes that have been paid ($3m in the above example) are associated with the dividend of $4m. Letting Tc denote the statutory company tax rate, Australian tax law allows the associated company tax to be as large as
providing that company taxes of that amount have been paid. So, with a dividend of $4m and a corporate tax rate of 30%, the maximum company tax that is associated with the dividend would be $1.714m. Since this does not exceed the company taxes of $3m, the figure of $1.714m would be associated with the dividend and is then treated as a pre-payment of personal tax by the company on behalf of its shareholders. Accordingly, it is called an imputation credit.
These imputation credits may or may not be useable by shareholders to reduce their personal tax obligations. Suppose that half of the shareholders cannot use the credits and the rest can. For those who can’t use the credits, and receive dividends of $2m, their personal tax obligation would be 35% of $2m ($0.7m), and therefore a post-tax dividend of $1.3m, as before. For those who can use the credits, and receive dividends of $2m (and therefore imputation credits of $0.857m), the personal tax obligation would be $0.143m and their post-tax dividend would be $1.857m, as follows:
Gross Dividend = Cash Dividend + Imputation Credits = $2m + $0.857m = $2.857m
Tax on Gross Dividend = $2.857m x 0.35 = $1m
Tax Obligation = Tax on Gross Dividend – Imputation Credits = $1m - $0.857m = $0.143m
Post tax Dividend = Cash Dividend – Personal Tax = $2m - $0.143m = $1.857m
So, the effect of imputation is to reduce personal tax for the shareholders who can use the imputation credits from $0.7m to $0.143m, and therefore raise their post-tax dividend from $1.3m to $1.857m.
The entire pre-tax profit of $10m can be categorised into the part that is paid in taxes, the part retained within the business, the part received as dividends net of taxes by shareholders who can’t use the imputation credits, and the part received as dividends net of taxes by shareholders who can use the imputation credits, as shown in Table 1 below. Importantly, the total tax rate (total taxes divided by pre-tax income) paid in respect of income distributed as dividends to shareholders who can use the imputation credits is 35%, which is the personal tax rate of these shareholders. For shareholders who can use the credits, one interpretation of this is that company taxes have been augmented by personal taxes, to achieve a total tax rate of 35% comprising company tax at 30% and additional personal tax at 5%. An alternative interpretation is that, for these shareholders, company tax has been completely supplanted by personal tax at their personal tax rate of 35%.
Three other important features of this example are as follows. Firstly, the total company taxes paid are $3m of which $1.714m has been reclassified as imputation credits. The proportion here is 57%, and is generally called the “distribution rate” for the imputation credits. Secondly, the rest of these company taxes ($1.286m) are called undistributed credits, and these might be attached to future dividends. Thirdly, of the imputation credits that have been attached to dividends (of $1.714m), half of these have been fully used by investors and the other half have been unused. Leaving aside the question of which investors are relevant, this proportion used (50%) is called the “utilisation rate”.
Table 1: Allocation of Income and Associated Taxes
______
Retained To Sholders To Sholders Total
Not Using ICs Using ICs
______
Pre-Tax Income$4.286m$2.857m$2.857m$10m
Company Tax at 30%$1.286m$0.857m$0.857m$3m
Post-Tax Profit$3m$2m$2m$7m
Dividend$2m$2m$4m
Dividend Tax$0.7m$0.143m$0.843m
Post-Tax Dividends$1.3m$1.857m$3.157m
Total Tax Rate54%35%38%
______
As noted this process can be interpreted in two equivalent ways. One interpretation is to consider shareholders who can use the credits to have paid personal taxes of $0.143m in addition to company taxes associated with their dividends of $0.857m, totalling $1m, as shown in the penultimate column of Table 1. The other interpretation is to consider the company taxes associated with these dividends as having been retrospectively set to zero and the entire taxes paid of $1m constituting personal taxes at the investor’s marginal tax rate of 35% (applied to the gross dividend). In this latter case, the company taxes that have effectively been paid are reduced to $2.143m, representing 21.4% of the pre-tax income of $10m. This effective tax rate Te of 21.4% is related to the statutory rate, the “distribution rate”, and the “utilisation rate” as follows:
where IC is the imputation credits for that company in the relevant period, TAX the company taxes paid by it, and U the utilisation rate.
2.2The Role of Imputation Credits in the Officer CAPM
The standard form of the CAPM (Sharpe, 1964; Lintner, 1965; Mossin, 1966) assumes inter alia that all forms of income from capital assets are equally taxed at the personal level. Whether this is inconsistent with dividend imputation depends upon how imputation is interpreted. If it is interpreted as a process that reduces the tax rate on cash dividends, corresponding to the first interpretation discussed in the previous section, then the standard form of the CAPM cannot apply and therefore must be displaced by a version that recognises that cash dividends are taxed at a lower rate than ordinary income (as in Lally, 1992, and Cliffe and Marsden, 1992). By contrast, if imputation is interpreted as a process that substitutes personal tax for corporate tax, corresponding to the second interpretation discussed in the previous section, then the standard CAPM is still valid. However, as shown in the previous section, the dividend tax rate now applies to gross dividends (cash dividends plus imputation credits, to the extent the latter can be used) rather than cash dividends and therefore dividends within the context of the CAPM must be defined in the same way. This is the approach adopted by Officer (1994), and used by all Australian regulators. Thus the equilibrium expected rate of return on equity is
(1)
where Rf is the risk free rate, the equity beta defined against the Australian market index, and the expected rate of return on the Australian market portfolio inclusive of imputation credits to the extent they can be used. Letting Sm denote the current value of the market portfolio, ICm the imputation credits on the assets included in the market portfolio, U the utilisation rate on the credits, and Rm the actual rate of return on the market portfolio excluding the imputation credits, then
(2)
Thus, when estimating the MRP, it is necessary to add the last term in this equation. Furthermore, and consistent with classifying some company tax as personal tax on dividends, being the distributed imputation credits to the extent that they can be utilised by investors, the cash flows that are discounted to yield the equity value of the company are accordingly higher. Letting S0 denote the current value of equity, S1 the expected value in one year, Y1 the expected cash flows over the first year to equity holders (net of all deductions except company taxes), TAX1 the expected company taxes over the first year, d the proportion of these company taxes that are distributed as imputation credits, and IC1 the distributed imputation credits over the first year, then S0 is the present value of Y1, S1, and TAX1 (net of that part distributed as imputation credits and utilised by investors), discounted using the Officer CAPMwith the MRP denoted:
(3)
Letting P1 denote the expected taxable income in the first year, then TAX1 is the product of P1 and the statutory corporate tax rate Tc, and therefore S0 is as follows:
where Te is the effective corporate tax rate referred to in the previous section. So, relative to the standard form of the CAPM, the Officer CAPMand the associated cash flows requires three additional parameters: the ratio of market-level imputation credits to the value of the market portfolio (ICm/Sm), the ratio of firm-level imputation credits to firm level company tax payments (IC/TAX) and the utilisation rate (U). The second of these parameters is called the “distribution rate” and the product of the last two is called “gamma”. Our concern in this paper is with the distribution rate and the utilisation rate.
The utilisation rate referred to here is a market-level parameter, i.e., the same value applies to each firm. Individual investors also have utilisation rates: one for those who can fully use the credits and zero for those who can’t. Consequently it might be presumed that U is some type of weighted average over investors. Although Officer (1994) provides no clarification on this matter, because his derivation of the model is intuitive rather than formal, Lally and van Zijl (2003, section 3) provide a formal derivation of a generalisation of Officer’s model (with the Officer model being a special case), in which variation of utilisation rates across investors is recognised. In this derivation, they show that U is a complex weighted average over all investors holding risky assets, where the weights involve each investor’s investment in risky assets and their risk aversion. Individual investors’ levels of risk aversion are not observable. Accordingly it is necessary to (reasonably) act as if risk aversion is uncorrelated with utilisation rate at the investor level, in which case the weights reduce to investors’ relative investments in risky assets, i.e., U is a value-weighted average over the utilisation rates of individual investors.